SOLUTION: Write the equation in polar coordinates. Then isolate the variable r when possible. x2 + y2 = 8x

Algebra ->  Vectors -> SOLUTION: Write the equation in polar coordinates. Then isolate the variable r when possible. x2 + y2 = 8x      Log On


   

Question 1080053: Write the equation in polar coordinates. Then isolate the variable r when possible.
x2 + y2 = 8x
Found 2 solutions by ikleyn, rapture:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
x = r%2Acos%28alpha%29,
y = r%2Asin%28alpha%29.    ====>


x%5E2+%2B+y%5E2 = r%5E2%2A%28cos%5E2%28alpha%29+%2B+sin%5E2%28alpha%29%29 = r%5E2.


Therefore, your equation in polar coordinates is 

r%5E2 = 8%2Ar%2Acos%28alpha%29.


Next, you can cancel "r" in both sides. Then you get your FINAL equation

r = 8%2Acos%28alpha%29.

Solved.


Answer by rapture(86) About Me  (Show Source):
You can put this solution on YOUR website!
Let x^2 + y^2 = r^2

Let x = rcosθ

x^2 + y^2 = 8x

r^2 = 8rcosθ

Divide both sides by r. This will isolate r.

(r^2)/r = (8rcosθ)/r

r = 8cosθ